This assumption allows us to study the spectral properties of the sample matrix using some tools from random matrix theory. Especially, when \(n(d) / d\)  converges to some constant \(\gamma \in (0, 1)\) , the Marchenko–Pastur law [1]} shows that \(\lambda _{\min } (\mathcal {X} \mathcal {X}^\top ) / n\)  converges to \((1 - \sqrt{\gamma })^2\)  almost surely. The non-asymptotic results are provided in [2]}.
